On Extremal Points of the Space of Symmetric Stochastic Matrices

Abstract

When uranium (U) is added to Y123 powders, after texturing the deposits containing U are found to be ∼300 nm. These deposits act as pinning centres, and increase J c by 90% per 0.8 wt% U. Neutron irradiation further increases J c . Total increases of J c by factors of e.g. ∼30 (at 77 K, 0.25 Tesla), and ∼15 (at 50 K, 10 Tesla) result. Magnitudes of J c are ∼290 000 A cm −2 (at 77 K, 0.25 T) and 10 6 A cm −2 (at 50 K, 0.25 T). The U/n process is not yet optimized. Chemistry, microstructure, radiation effects and cost are discussed.

Properties of Uniform Doubly Stochastic Matrices

“…There are other polytopes with similarly nice descriptions. For example, the symmetric doubly stochastic matrices have extreme points 1 2 (A σ + A T σ ) with A σ the permutation matrix of σ [14,40]. Perhaps the methods and results of our paper can be used to study the behavior of a randomly chosen point in these polytopes.…”